A380316 Sphenic numbers that are the sum of two successive sphenics.
385, 555, 759, 897, 935, 957, 1185, 1245, 1265, 1335, 2015, 2037, 2185, 2211, 2261, 2379, 2607, 2821, 2877, 2937, 3059, 3298, 3363, 3434, 3485, 3507, 3538, 3815, 3913, 4029, 4255, 4378, 4433, 4526, 4615, 4738, 4795, 4947, 5181, 5205, 5395, 5405, 5523, 5681, 5829, 5883, 6226
Offset: 1
Keywords
Examples
385 = 5*7*11 is a member because 385 = 190+195, sum of 18-th and 19-th sphenic number. 555 = 3*5*37 is a member because 555 = 273+292, sum of 28-th and 29-th sphenic number.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Maple
issphenic:= proc(n) local F; F:= ifactors(n)[2]; F[..,2] = [1,1,1] end proc: S:= select(issphenic, [$1..10000]): select(issphenic, S[1..-2]+S[2..-1]); # Robert Israel, Jan 20 2025
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Mathematica
sphenicQ[n_] := FactorInteger[n][[;; , 2]] == {1, 1, 1}; Select[MovingMap[Total, Select[Range[3200], sphenicQ], 1], sphenicQ] (* Amiram Eldar, Jan 21 2025 *) -
PARI
issphenic(n) = my(f=factor(n)); (bigomega(f)==3) && (omega(f)==3); lista(nn) = my(v=select(issphenic, [1..nn])); select(issphenic, vector(#v-1, k, v[k]+v[k+1])); \\ Michel Marcus, Jan 20 2025
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PARI
sphen(lim)=my(v=List(), t); forprime(p=2, sqrtnint(lim\=1,3), forprime(q=p+1, sqrtint(lim\p), t=p*q; forprime(r=q+1, lim\t, listput(v, t*r)))); Set(v) has(n,f=factor(n))=f[,2]==[1,1,1]~ list(lim)=my(v=List(),u=sphen(lim\2)); for(i=2,#u, if(has(u[i]+u[i-1]), listput(v,u[i]+u[i-1]))); forfactored(k=lim\2+1,lim\1-u[#u], if(has(0,k[2]), if(has(k[1]+u[#u]), listput(v,k[1]+u[#u])); break)); Vec(v) \\ Charles R Greathouse IV, Jan 21 2025
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